Geometry

Question Analysis

This question focuses on determining if  and  are similar using the AA (Angle - Angle), SSS (Side - Side - Side), and SAS (Side - Angle - Side) Triangle Similarity Theorems. Given the angles in the triangles, we can use the AA criterion by finding the remaining angles and checking for angle - angle equalities.

Key Concept Explanation

AA (Angle - Angle) Similarity Theorem: If two angles of one triangle are equal to two angles of another triangle, then the two triangles are similar.

SSS (Side - Side - Side) Similarity Theorem: If the ratios of the lengths of the three pairs of corresponding sides of two triangles are equal, then the two triangles are similar.

SAS (Side - Angle - Side) Similarity Theorem: If two sides of one triangle are proportional to two sides of another triangle and the included angles are equal, then the two triangles are similar.

Step - by - Step Solution

1. Find the measure of :

In , since the sum of angles in a triangle is , and , , then .

2. Find the measure of :

In , , , so

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